On the Braids for 8 10 Knot

Bu makale 8jo düğümü ve onun örgüsü ile ilgilidir. Düğüm teorisinde önemli kavramlardan birisi olan örgü kavramını kullanarak 8jo düğümünün örgüsü­nün Artin ve Garside temsilini elde edeceğiz. Daha sonra pozitiflik kavramı irdele­necektir

On the Braids for 8 10 Knot

This paper is concerned with 810 knots and its braids. The braids structure is very important role in Knots Theory. In view of this structure, we obtained braids for that knot and we will give the representations of Artin and we examine Garside Word problem. And then we will examine the positivity structure for these knots.

___

  • ARTIN, E. (1925).Theorie der Zopfe Hamburg Abh. 4, 47-72.
  • BIRM AN, J., K.H. KO and S.J. LEE (1998). “A New Aproach To The Word And Conjugacy Problems In The Braid Group”, Advances In Mathematics, vol. 139, (issue 2), 322-353.
  • BIRM AN, J. (1974). Braids,Links and M apping Class Groups, Princeton Universty Press.
  • BUSKIRK, J.V. (1983). “Positive Knots Have Positive Conway Polynomials”, Springer Lecture Notes in Mathematics, 1144, 146-159.
  • GARSIDE, F.A. (1969). “The Braid Group and Other Groups”, Quarterly Journal o f M athematics, 20 No 78, 235-254.
  • MURASUGI., K. (1996). Knots Theory and Its Applications, Birkhauser: Boston.
  • PATERSON, M. S., and A.A. RASBOROV (1991). “The Set M inimal Braids is co_NP-Complete”, Journal o f Algorithms, 12, 393-408.